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A New Payment Rule for Core-Selecting Package Auctions


  • Aytek Erdil

    () (Dept of Economics, University of Oxford, Oxford)

  • Paul Klemperer

    () (Dept of Economics, University of Oxford, Oxford)


We propose a new, easy-to-implement, class of payment rules, “Reference Rules,” to make core-selecting package auctions more robust. Small, almost riskless, profitable deviations from “truthful bidding” are often easy for bidders to find under currently-used payment rules. Reference Rules perform better than existing rules on our marginal-incentive-to-deviate criterion, and are as robust as existing rules to large deviations. Other considerations, including fairness and comprehensibility, also support the use of Reference Rules.

Suggested Citation

  • Aytek Erdil & Paul Klemperer, 2009. "A New Payment Rule for Core-Selecting Package Auctions," Economics Papers 2009-W11, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0911

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    References listed on IDEAS

    1. Peter Cramton, 2013. "Spectrum Auction Design," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 42(2), pages 161-190, March.
    2. Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
    3. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    4. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    5. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    6. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    7. Robert W. Day & S. Raghavan, 2007. "Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions," Management Science, INFORMS, vol. 53(9), pages 1389-1406, September.
    8. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
    9. Lawrence M. Ausubel & Peter Crampton & Paul Milgrom, 2004. "The Clock-Proxy Auction: A Practical Combinatorial Auction Design," Discussion Papers 03-034, Stanford Institute for Economic Policy Research.
    10. Paul Klemperer, 2010. "The Product-Mix Auction: A New Auction Design for Differentiated Goods," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 526-536, 04-05.
    11. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
    12. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.
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    More about this item


    multi-object auction; core; combinatorial auction; package auction; core-selecting auction; Vickrey auction; Vickrey; simultaneous ascending auction; robust design.;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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